advanced_tools:gauge_symmetry
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advanced_tools:gauge_symmetry [2018/05/13 09:19] jakobadmin ↷ Links adapted because of a move operation |
advanced_tools:gauge_symmetry [2018/07/24 10:20] 129.13.36.189 [FAQ] |
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| The computations can be different in different coordinate systems and usually, one picks a coordinate system where the computation is especially simple. However, the physics that we are describing, of course, doesn't care about how we describe it. It stays the same, now matter how we choose our coordinate system. | The computations can be different in different coordinate systems and usually, one picks a coordinate system where the computation is especially simple. However, the physics that we are describing, of course, doesn't care about how we describe it. It stays the same, now matter how we choose our coordinate system. | ||
| - | In modern physics, we no longer describe what is happening merely through the position of objects at a given time, as we do it in classical mechanics. Instead, we use abstract objects called fields. The best theory of what is happening in nature at the most fundamental level is [[theories:quantum_field_theory:canonical]]. Like the electromagnetic field, these fields can get excited (think: we can produce a wave or ripple of the field). For example, when we excite the electron field we "produce" an electron. | + | In modern physics, we no longer describe what is happening merely through the position of objects at a given time, as we do it in classical mechanics. Instead, we use abstract objects called fields. The best theory of what is happening in nature at the most fundamental level is [[theories:quantum_field_theory:canonical|quantum field theory]]. Like the electromagnetic field, these fields can get excited (think: we can produce a wave or ripple of the field). For example, when we excite the electron field we "produce" an electron. |
| The fields themselves are abstract mathematical entities that are introduced as convenient mathematical tools. With these new mathematical entities comes a new kind of freedom. Completely analogous to how we have the freedom to choose the orientation and the location of the origin of our coordinate system, we now have freedom in how we define our fields. | The fields themselves are abstract mathematical entities that are introduced as convenient mathematical tools. With these new mathematical entities comes a new kind of freedom. Completely analogous to how we have the freedom to choose the orientation and the location of the origin of our coordinate system, we now have freedom in how we define our fields. | ||
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| - | --> What conserved quantities follow from gauge symmetries?# | ||
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| - | Using [[theorems:noethers_theorems|Noether's first theorem]] we find that the conserved charges that would follow from invariance under gauge transformations are identically zero. This is shown, for example, in section 3.4.1 [[http://math.ucr.edu/home/baez/classical/texfiles/2005/book/classical.pdf|here]]. | ||
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| - | However, using Noether's second theorem we can derive relations between our equations of motion, that are known as Bianchi identities. | ||
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| - | <-- | ||
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| --> Is a gauge symmetry really a symmetry?# | --> Is a gauge symmetry really a symmetry?# | ||
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| + | --> What conserved quantities follow from gauge symmetries?# | ||
| + | Using [[theorems:noethers_theorems|Noether's first theorem]] we find that the conserved charges that would follow from invariance under gauge transformations are identically zero. This is shown, for example, in section 3.4.1 [[http://math.ucr.edu/home/baez/classical/texfiles/2005/book/classical.pdf|here]]. | ||
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| + | However, using Noether's second theorem we can derive relations between our equations of motion, that are known as Bianchi identities. | ||
| + | |||
| + | |||
| + | <-- | ||
advanced_tools/gauge_symmetry.txt · Last modified: 2020/04/02 20:12 by 95.90.205.199
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